NO Non-Confluence Proof

Non-Confluence Proof

by Hakusan

Input

The rewrite relation of the following TRS is considered.

inv(0) 0
inv(s(x)) p(inv(x))
inv(p(x)) s(inv(x))
minus(x,0) x
minus(x,p(y)) s(minus(x,y))
minus(x,s(y)) p(minus(x,y))
minus(0,x) inv(x)
minus(s(x),s(y)) minus(x,y)
minus(p(x),p(y)) minus(x,y)
inv(x) minus(0,x)
s(p(x)) x
p(s(x)) x

Proof

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = minus(p(x1),p(y2))
ε minus(x1,y2)
= t1

t0 = minus(p(x1),p(y2))
ε s(minus(p(x1),y2))
= t1

The two resulting terms cannot be joined for the following reason:

Tool configuration

Hakusan